A projected discrete Gronwall's inequality with sub-exponential growth

作者：Zhou Linfeng; Zhang Weinian^*

来源：Journal of Difference Equations and Applications, 2010, 16(8): 931-943.

DOI：10.1080/10236190802612873

• Gronwall's inequality
• difference equation
• sub-exponential growth
• non-monotonicity
• (h, k)-dichotomy

Along with the increasing interest in (h, k)-dichotomy, more attentions are paid to sub-exponential growth in research of asymptotic behaviours. In this paper, we generalize a projected discrete Gronwall's inequality given in [J. Differ. Equ. Appl. 10 (2004), 661-689] to a general one, which may include both terms of sub-exponential growth inside the summation and non-monotonic terms outside the summation. We demonstrate our results with concrete non-monotonic functions and sub-exponential functions. We apply our results to estimating bounded solutions of a non-linear difference equation with an (h, k)-dichotomy.

• 出版日期2010
• 单位四川大学